Government plans to cut spending in Whitehall departments and invest an extra £5 billion in schools and other capital projects will "make our country work better", Prime Minister David Cameron has said.

The new investment, to be confirmed by Chancellor George Osborne's Autumn Statement on Wednesday, will include £1 billion to build 100 new academies and free schools over the next two years.

Labour said the announcement was an effective admission that the coalition Government's cuts in infrastructure spending since the 2010 election have been "a catastrophic mistake" which have weakened the economy. But Conservative sources insisted that the coalition was spending billions more on capital projects than the Labour plans that it inherited.

Mr Osborne and Chief Secretary Danny Alexander have briefed the Cabinet on the plans for additional investment in transport, skills, science and schools. To fund the programme without extra state spending, Whitehall departments will be told to cut day-to-day spending by 1% (£950 million) in 2013/14 and 2% (£2.5 billion) in 2014/15. But health, schools, international aid, HM Revenue and Customs and nuclear decommissioning will be protected.

Speaking on a visit to a south London school with Deputy Prime Minister Nick Clegg, Mr Cameron said: "Government departments aren't actually spending up to their budgets so I think we can say to them 'You've got to cut back some spending, including some unnecessary spending', and let's put that money into things that will make a difference in our country and in our economy - more roads, more school buildings, more infrastructure to make our economy work better, to make our country work better."

The changes apply directly to England only, but there will be knock-on effects for Scotland, Wales and Northern Ireland under the complicated formula which determines central funding for the different parts of the United Kingdom.

Local government will be exempted from the cuts in the first year, as it is already having to find savings to deliver a council tax freeze, but councils will be required to meet the 2% cut in 2014/15.

Meanwhile, the Ministry of Defence will be given additional flexibility to roll over underspends - which last year amounted to almost £400 million - from one year to the next. As a result, ministers believe that there will be no reduction in military manpower and core MoD budgets.

The decision to inflict further cuts on Whitehall budgets comes after a mid-term spending assessment carried out by Mr Alexander, which found that departments have underspent by a total of £3 billion over the last two years.

Labour's Treasury spokeswoman Rachel Reeves said: "The Chancellor seems to have finally admitted that abolishing the Building Schools for the Future programme and his other deep cuts to infrastructure investment were a catastrophic mistake which cost jobs and weakened our economy."